Antenna Fundamentals

HTEL 104 Antenna Fundamentals The antenna is the essential link between free space and the transmitter or receiver. As such, it plays an essential part in determining the characteristics of the complete system. The design of the antenna and its working environment will decide its effectiveness in any particular system. In Antennas (2nd ed), John D Kraus defined an antenna as: "A structure that transforms electromagnetic energy contained in a guided wave to that of free-space propagation or vice versa." THE ELECTROMAGNETIC WAVE An electromagnetic wave in free space comprises electric (E) and magnetic (H) components perpendicular to each other. If the x co-ordinate is taken along the line in the direction of wave travel, then the E and H field vectors lie entirely in the yz plane as shown in Fig 13.1. The wave front is a plane surface normal to the direction of propagation and is called a transverse electromagnetic wave (TEM). It can best be envisaged as the surface of a rapidly inflating balloon, otherwise known as a wave front, however, a small area of this expanding surface can be regarded as flat plane at a distance from the source. A TEM wave, in which the electric and magnetic vectors, while varying in magnitude and sign, remain along the same axis in space is said to be polarised, the plane of polarisation (by convention) being that contained in the electric vector, ie the xy plane in Fig 13.1.. Polarisation is discussed in more detail later. The wave illustrated in Fig 13.1 travelling in free space is unrestricted in its motion and is known a travelling wave. Near and Far-Field Antenna Regions The TEM wave described above is formed some distance away from the antenna in a region known as the far field. In this region the total electric and magnetic fields are at right-angles to each other and to the direction of propagation, and their respective maxima are phased 90 (one quarter-wavelength) apart as shown in Fig 13.1. In space, the ratio of the E/H fields yields a value of 377 ohms, which is the impedance of free space. At distances closer to the antenna, the fields become more complex, and there are additional field components directed along the direction of propagation. This is the near field region, Fig 13.2: Near and far fields of an antenna in which coupling between the antenna and adjacent conductive structures (power wires, plumbing or other antennas) becomes significantly greater than would apply from illumination by a freely propagating electromagnetic wave. Conductive objects within the near field of an antenna can seriously affect both its radiation pattern and its input impedance. The elements of antenna arrays usually lie within the near field of adjacent elements, and the mutual coupling between them must be taken into account if the best overall gain is to be achieved. Radiation pattern, input impedance and mutual coupling will described later. The approximate near/far field boundary is defined as: R=2L 2 /wavelength Where R is the distance and L is the length of the antenna as illustrated in Fig 13.2. RESONANCE If an oscillatory current is passed along a wire, the electric and magnetic fields associated with it can be considered as a wave attached to the wire and travelling along it. If the wire finally terminates in an insulator the wave cannot proceed but is reflected. This reflection is an open-circuit reflection and produces standing-wave fields on the wire. How these standing waves are produced is described in the chapter on Transmission Lines. Fig 13.3 shows two typical cases where the wire is of such a length that a number of complete cycles of the standing wave can exist along it. Since the end of the wire is an open-circuit, the current at that point must be zero and the voltage a maximum. Therefore at a point one quarter-wavelength from the end, the current must be a maximum and the voltage will be zero. At positions of current maxima, the current-to-voltage ratio is high Fig 13.1: Conceptual diagram of Transverse Electromagnetic (TEM) Wave Fig 13.3: Standing waves on resonant antennas, showing voltage and current variations along the wire at its fundamental resonant frequency and at second harmonic frequency

and the wire will behave as a low-impedance circuit. At voltage maxima the condition is reversed and the wire will behave as a high-impedance circuit. A wire carrying a standing wave as illustrated in Fig 13.3 exhibits similar properties to a resonant circuit and is also an efficient radiator of energy. This is a resonant or standing wave antenna and the majority of the antennas met with in practice are of this general type. The length for true resonance is not quite an exact multiple of the half-wavelength because the effect of radiation causes a slight retardation of the wave on the wire and also because the supporting insulators may introduce a little extra capacitance at the ends. An approximate formula suitable for wire antennas is: Length (m) = 155(n - 0.05)/f or Length (feet) = 485(n - 0.05)/f Where n is the number of complete half-waves in the antenna and f is the frequency in megahertz. It must be emphasised that an antenna does not have to be resonant to radiate. Radiation takes place from any elevated wire carrying a radio frequency current; if this wire is terminated in a resistor the wave will be a travelling wave rather than a resonant one. Radiation will always occur unless prevented by screening or cancelled by an opposing field of equal magnitude, as occurs in transmission lines. RADIATION RESISTANCE When power is delivered from the transmitter into the antenna, some small part will be lost as heat, since the material of which the antenna is made will have a finite resistance, and a current flowing in it will dissipate some power. The bulk of the power will usually be radiated and, since power can only be consumed by a resistance, it is convenient to consider the radiated power as dissipated in a fictitious resistance which is called the radiation resistance of the antenna. Using ordinary circuit relations, if a current I is flowing into the radiation resistance R, then a power of I 2 R watts is being radiated. As depicted in Fig 13.3 the RMS current distribution along a resonant antenna or indeed any standing wave antenna is not uniform but is approximately sinusoidal. It is therefore necessary to specify the point of reference for the current when formulating the value of the radiation resistance, and it is usual to assume the point of maximum current. A halfwave dipole in free space has a radiation resistance of about 73Ω. If it is made of highly conductive material such as copper or aluminium, the loss resistance may be less than one ohm. The conductor loss is thus relatively small and the antenna provides an efficient coupling between the transmitter and free space. FEED IMPEDANCE When the antenna is not a resonant length, it behaves like a resistance in series with a positive (inductive) or negative (capacitive) reactance and requires the addition of an equal but opposing reactance to bring it to resonance, so that it may be effectively supplied with power by the transmitter. The combination of resistance and reactance, which would be measured at the antenna terminals with an impedance meter, is referred to in general terms as the antenna input impedance. This impedance is only a pure resistance when the antenna is at one of its resonant lengths. Fig 13.4 shows, by means of equivalent circuits, how the impedance of a dipole varies according to the length in wavelengths. It will be seen that the components of impedance vary Fig 13.4: Typical input impedance (Zi) value for dipoles of various lengths Fig 13.5: The input resistance (fixed point impedance) of a halfwave dipole is low at (a) and high at (b) over a wide range. The input impedance of the antenna is related specifically to the input terminals, whereas the radiation resistance is usually related to the point of current maximum. It is possible to feed power into an antenna at any point along its length so that the input impedance and the point of current maximum even of a resonant antenna may be very different in value, although in this case both are pure resistances. Only when the feed point of the antenna coincides with the position of the current maximum on a single wire will the two be approximately equal, Fig 13.5(a). If the feed point occurs at a position of current minimum and voltage maximum, the input impedance will be very high, but the the point of current maximum remains unaltered Fig 13.5(b). For a given power fed into the antenna, the actual feed-point current measured on an RF ammeter will be very low because the input impedance is high. Such an antenna is described as voltage fed. Earlier it was stated that a centre fed halfwave dipole in free space has a radiation resistance of about 73Ω. However, the impedance presented at the feed point by an antenna is a complex function of the size and shape of the antenna, the frequency of operation and its environment. The impedance is affected by the proximity of other conducting objects, where the induction of RF currents alters the impedance through mutual coupling between the antenna and object. The elements of a Yagi antenna are mutually coupled together, and the driven element would present a very different impedance if measured in isolation from the rest of the structure. RADIATION PATTERNS, DIRECTIVITY AND GAIN The performance of an antenna can be assessed by its radiation pattern. A VHF base station or repeater usually requires antennas that distribute the signal equally in all directions, whilst a station configured for DX operation will require antennas that focus the energy in one particular direction. Methods of achieving focus of energy are described later. Such a pattern can be made by energising the antenna with a known level of RF power and then performing a large number of 13.2

(a) Fig 13.6: Three-dimensional free-space polar diagrams for (a) an isotropic radiator and (b) a dipole field strength measurements at various angles, then plotting the results on a polar graph to produce an azimuth polar diagram. This diagram would then present the relative field strength or power intensity as a radial distance from the centre of the graph at the relevant angle. The directivity of an antenna is the ratio of maximum radiation intensity to the average intensity. The isotropic antenna, see below, radiates equally in all directions and has directivity of 1, a theoretical minimum. The smaller the three-dimensional beam angle the greater the directivity. If one antenna system can be made to concentrate more radiation in a certain direction than another antenna for the same total power supplied, it is said to exhibit gain over the other antenna in that direction. The gain of an antenna is a combination of directivity and efficiency when compared with a reference antenna. If an antenna were minutely small and radiated equally in all three dimensions the overall radiation pattern would be a sphere. Although the construction of such an antenna is not possible it is used as a theoretical entity in antenna mathematical modelling and is known as an isotropic source; it is used as a theoretical reference for measuring antenna gain. Gain or loss relative to an isotropic radiator is stated in dbi. A radiation pattern of an isotropic source is shown in Fig 13.6(a). The simplest practical form of antenna is the dipole. Although this antenna may be of any length, the word 'dipole' usually implies a half-wavelength long resonant antenna, fed via a balanced feeder at the centre. The dipole antenna does not radiate equally in all directions because the current along its length is not constant and it produces a three-dimensional doughnut shaped radiation pattern. This pattern and a polar diagram section is shown in Fig 13.6(b). (c) Fig 13.7: Radiation of a 12-element VHF Yagi antenna using (a) Polar format, ARRL logarithmic decibel scale. (b) Polar format, linear db scale. (c) Rectangular format, linear db scale 13.3

Because of its simplicity the dipole itself has become a reference standard and has a power gain of 2.15dbi. Gain figures, using the dipole radiator as a reference, are symbolised dbd. A practical antenna may have good directivity, but low gain if the antenna has losses through poor design, the use of lossy components or poor mechanical construction. If the antenna were lossless, the gain and directivity would be the same. Sections through a three-dimensional radiation pattern are normally either vertical (elevation) or horizontal (azimuth). The diagrams so far discussed ignore the effects of ground that could affect the diagram with reflections. Such diagrams are called free space diagrams, and like the isotropic antenna, are theoretical and only used in antenna mathematical models. Radiation patterns that include the effects of ground are described later in Computer Modelling. Polar diagrams in early antenna literature used polar graphs plotted on a linear scale. This enabled the main lobe beamwidth to be measured but sidelobes were barely visible. The ARRL has promoted the use of a hybrid polar chart, Fig 13.7(a), which combines features of both linear and logarithmic radial scaling in decibels [1], which is used in most amateur radio publications these days. The logarithmically scaled chart, Fig 13.7(b), clearly shows the levels of the sidelobes at the expense of the main lobe. There is also the more specialised rectangular format, Fig 13.7(c), which uses the linear db scale. The vertical axis of the rectangular plot represents the relative field strength or power density as a function of the angle shown on the horizontal axis. This presentation is useful for high-gain VHF/UHF antennas as a lack of symmetry can be easily seen, and is often an indication of loss of efficiency or incorrect feeding of multiple-element arrays The radiation pattern characteristics of directional antennas are usually expressed as the beamwidth in two principal planes at right angles to each other. The beamwidth in these principal planes is usually defined as the angle including the main beam at which the radiated energy falls to one half the maximum level. This is called the half-power beamwidth, and the points on the radiation pattern are often called the 3dB or half-power points of the radiation pattern, being 3dB below the main beam as shown in Fig 13.8. Key features of the radiation patterns of the antenna shown in Fig 13.8 are the main lobe or main beam, and the presence of Fig 13.8: Typical polar diagram of a Yagi antenna several sidelobes including one pointing in the opposite direction to the main lobe. The front-to-back or F/B ratio is the ratio of the energy radiated by the peak of the main lobe to that in the opposite direction, and is often used as an estimate of the 'goodness' of a beam antenna. This ratio is usually expressed in decibels. As more power is radiated in minor lobes, less power is available in the main lobe, and the gain of the antenna is reduced. Whilst gain is usually measured by direct substitution of the antenna under test with a reference antenna, it is possible to estimate the directivity of directional antennas with fair accuracy if the half-power beamwidths can be measured in the principal (E and H) planes of the main beam. If the antenna losses can be assumed to be very small, the gain will be essentially equal to the calculated directivity. Measuring techniques with readily available amateur radio equipment are described in [2]. POLARISATION Earlier it was stated that the plane of polarisation was, by convention, contained in the electric component of a TEM wave. A linear dipole generates the electric component of the TEM wave along its axis so this antenna, or linear antenna array, oriented vertically with respect to earth is said to be vertically polarised. The same antenna oriented horizontally is horizontally polarised. Polarisation is important on paths that don't alter the transmitted polarisation (a line-of-sight VHF/UHF or microwave link, for example). Two such antennas must be co-polarised (polarised in the same direction) in order to communicate; totally cross-polarised antennas theoretically cannot communicate. They are also important when making antenna measurements on an antenna range. For HF antennas, polarisation is not so important because polarisation is altered when a TEM wave is refracted by the ionosphere. Satellite users on VHF/UHF often use circular polarisation to reduce the effects of propagation, ground reflections or the spinning motions of the satellites on the signals. The effect of circular polarisation can be visualised as a signal that would be radiated from a dipole that is spinning about its centre at the radiating frequency. The tip of the electric vector traces out a corkscrew as it propagates away from the antenna and, like a corkscrew, the polarisation is described as right- or left-handed circular, dependent on the direction of rotation of the electric vector as seen from the transmitter. Methods for generating circular polarisation are shown in the chapter on practical VHF/UHF antennas. A fixed linear dipole will receive an equal signal from a circularly polarised wave whether it is mounted vertically, horizontally or in an intermediate position, if there are no ground reflections. The signal strength will be 3dB less than if a circularly polarised antenna of the same sense is used; however, a circularly polarised antenna of the opposite sense will receive no signals. Both these effects are due to polarisation mismatch between the wave and the receive antenna. BANDWIDTH There are no unique definitions for antenna bandwidth. Dependent upon the operational requirements of the antenna, the definitions fall into two categories: radiation pattern bandwidth and impedance bandwidth. 13.4

Total field 0dB 28.5MHz 29MHz 29.5MHz 10dB 20dB Radiation Pattern Bandwidth Antenna radiation patterns are dependent upon the operating frequency. Their sensitivity to frequency changes are in turn dependent on the degree of tuning or inherent Q required to achieve the desired characteristic. Bandwidth is defined as the frequency range over which satisfactory performance can be obtained. The criteria for defining bandwidth could be one or more of the following: Main lobe beamwidth Acceptable sidelobe level Minimum gain or directivity Polarisation qualities With the relatively limited frequency range within the amateur bands, the gain normally does not change too radically with frequency, although this is not always the case with very-high-gain VHF/UHF Yagi antennas where the gain and the pattern shape or direction of radiation may be stable over only a very narrow frequency band. An example of this is shown in Fig 13.9. For beam antennas, such as the Yagi, the radiation pattern bandwidth is often defined as the frequency range over which the main lobe gain decreases to 1dB below its maximum value. This is not to be confused with main lobe directivity beamwidth, described earlier For electromagnetically simple, small antennas (ie when the linear dimensions are of the order of half a wavelength or less) EZNEC+ Fig 13.9: Variation in free-space radiation pattern of a three-element Yagi antenna 30dB the limiting factor is normally the input impedance. With circular polarisation antennas the change of the polarisation characteristic with frequency is often the limiting factor. In endfire linear arrays, collinears and the like, the main lobe direction and shape can change considerably before the gain deteriorates significantly. For any antenna array or multiply fed antenna, the limiting factors may be determined by the ability of the feed arrangements to maintain the correct current distribution to the antenna elements as the frequency is varied. Such antennas bandwidths may also be limited by excursions of input impedance, as described below. Impedance Bandwidth The impedance bandwidth of an antenna is defined as the frequency range over which the antenna impedance results in a standing wave ratio (SWR) less than some arbitrary limit. This may be typically 1.5:1 or 2:1 for amateur operation with solid-state transmitters, or higher values for other applications. The impedance bandwidth can be very narrow on electrically small antennas such as HF mobile antennas, as shown in Fig 13.10. Ideally, an antenna should be impedance matched to the feedline and thence to the transmitter or receiver. Although tuned feed arrangements are often used at HF, where a high standing wave ratio may be acceptable on the feedline, the losses in VHF feeders and tuning components usually preclude this approach at VHF and UHF. Impedance bandwidth and radiation pattern bandwidth are independent of each other. It is quite possible for the impedance bandwidth to be greater than the radiation pattern bandwidth, especially with high-gain antennas, and to be able to feed power into an antenna that is then wasted by radiating it in other than the desired direction. THE EFFECT OF GROUND The ground under the antenna acts as a reflector. Electromagnetic waves from the antenna radiate in all directions and some of these waves are reflected by ground. If the reflected wave is in phase, or partially in phase, with a direct wave it enhances radiation and increases gain at a particular angle. Other combinations of reflected and direct waves, whose phases tend to cancel, reduce gain at other angles. Waves A and C shown in Fig 13.11 enhance gain while B and C tend to cancel and reduce the gain. This is the cause of the Fig 13.10: Comparative SWR curves of two commercial antennas. Assuming a SWR limit of 2:1, the Texas Bugcatcher antenna has a bandwidth of 12kHz on 80m Fig 13.11: The effect of ground reflection on directly radiated waves 13.5

familiar vertical antenna patterns. This aspect is most important and has implications viewing any horizontal polar diagram of a practical antenna. It is also important that ground effects are taken into consideration when setting up equipment on an antenna range. Consider the three-dimensional polar diagram of a three-element beam in Fig 13.12(a). If we take a vertical or elevation cross section of this diagram it produces the familiar elevation diagram shown in Fig 13.12(b). Determining the horizontal diagram is not as easy; it can not be plotted through the true horizontal because of the effect of ground (theoretically the radiation strength will be zero in the horizontal plane although this is not the case in practice). The practical solution is to plot the horizontal diagram at the angle of maximum radiation of the main lobe as shown in Fig 13.13. Fig 13.12: (a) Three-dimensional polar diagram of a three-element beam, showing a vertical section at the angle of maximum radiation. (b) Elevation diagram resulting from this section ANTENNA MODELLING USING A COMPUTER Modelling is the technique of evaluating the performance of one object or system by evaluating the performance of a substitute called a model. Models can be physical objects, like a VHF scale model sometimes used to evaluate a HF antenna. Models can also be purely mathematical, like the equations used in circuit analysis. The following discussion describes a mathematical model on your personal computer using readily available software. Fig 13.13: Three-dimensional polar diagram of a three-element beam showing: (a) A horizontal conical section at the angle of maximum radiation. (b) Diagram at the angle of maximum radiation. (c) Diagram at an angle other than that of maximum radiation 13.6